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# 6.5 - OUTLINE Homework(and homework questions Homework Ask...

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Unformatted text preview: OUTLINE Homework (and homework questions) Homework Ask any review questions you want Ask Review long division, solve by factoring and graphing calculators and BREAK 6.5 Notes (not on quiz) 6.5 Homework time / study time Homework Homework: Quiz Friday! About 40-50 50 pts pts Key is online! Class notes are online! Key Questions? Questions? Review Long division (2 x 3 − 4 x 2 − 6 x + 8) ÷ (2 x − 2) Review Solve by Factoring 125 x 3 − 27 1 Graphing calculators Find all the real zeros of each Section 6.5 Rational Root Theorem! y = 2x − 3 3 y = x + 3x − 1 4 3 How many roots or zeros should each have? have? Objectives Use the rational, irrational, and imaginary root theorems to locate all the roots of a all the given polynomial equation given Rational Root Theorem This only works if we have integer coefficients. coefficients. Possible rational roots = p q Find the rational roots of x 3 + x 2 − 3x − 3 = 0 List the possible rational roots: possible Test using substitution or synthetic division division Use the rational root Use theorem to find ALL roots theorem 2x3 − x 2 + 2x −1 = 0 2 Use the rational root Use theorem to find ALL roots theorem x 3 − 2 x 2 − 5 x + 10 = 0 The Irrational Root The Theorem Theorem If a + b is a root of a polynomial a− b equation with rational coefficients, then the conjugate is also a root the In other words, irrational roots occur in conjugate pairs. If If 3 is a root, then − 3 is a root The Imaginary Root The Theorem Theorem If the imaginary number a + bii iis a root of bs a polynomial equation with real coefficients, then the conjugate a – bi bi also is a root also Imaginary roots also occur in conjugate also occur pairs pairs If 3, 7 and 2 − i are roots of a polynomial with integer coefficients, find two additional roots. two What is the degree of this polynomial? What Find a third-degree polynomial equation degree with rational coefficients that has roots 3 and 1 + i Homework Page 333 (1-3), 7, 8, 11, (16-18), 23, 24 Page 18), (32-36) even (32 Due Monday Due 3 ...
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